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On polynomials in primes and J. Bourgain's circle method approach to ergodic theorems

Published online by Cambridge University Press:  19 September 2008

R. Nair
R. Nair
Affiliation:
Department of Pure Mathematics, University of Liverpool, PO Box 147, Liverpool L69 3BX, UK
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Extract

In this paper we prove the following theorem.

Theorem 1. For a measure-preserving system (X, β, μ, T) and a positive integer k, if f ∈ L2(X, β, μ), the averages

,

converge μ almost everywhere. Here p runs over the rational primes and πN denotes their number in [1, N].

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 3 , September 1991 , pp. 485 - 499
Copyright
Copyright © Cambridge University Press 1991

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References

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